Related papers: Identifiability in Two-Layer Sparse Matrix Factori…
Factor analysis is a statistical technique that explains correlations among observed random variables with the help of a smaller number of unobserved factors. In traditional full factor analysis, each observed variable is influenced by…
Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss…
Factor analysis is a widely used technique for dimension reduction in high-dimensional data. However, a key challenge in factor models lies in the interpretability of the latent factors. One intuitive way to interpret these factors is…
The convergence of the conjugate gradient method for solving large-scale and sparse linear equation systems depends on the spectral properties of the system matrix, which can be improved by preconditioning. In this paper, we develop a…
We consider two matrix completion problems, in which we are given a matrix with missing entries and the task is to complete the matrix in a way that (1) minimizes the rank, or (2) minimizes the number of distinct rows. We study the…
We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…
The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
There has been increased research interest in the subfield of sparse Bayesian factor analysis with shrinkage priors, which achieve additional sparsity beyond the natural parsimonity of factor models. In this spirit, we estimate the number…
Matrix factorization models have been extensively studied as a valuable test-bed for understanding the implicit biases of overparameterized models. Although both low nuclear norm and low rank regularization have been studied for these…
Constrained tensor and matrix factorization models allow to extract interpretable patterns from multiway data. Therefore identifiability properties and efficient algorithms for constrained low-rank approximations are nowadays important…
This paper introduces the multidimensional butterfly factorization as a data-sparse representation of multidimensional kernel matrices that satisfy the complementary low-rank property. This factorization approximates such a kernel matrix of…
Supervised classification and representation learning are two widely used classes of methods to analyze multivariate images. Although complementary, these methods have been scarcely considered jointly in a hierarchical modeling. In this…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
We consider the problem of recovering a matrix from its action on a known vector in the setting where the matrix can be represented efficiently in a known matrix dictionary. Connections with sparse signal recovery allows for the use of…
Matrix factorization techniques have been widely used as a method for collaborative filtering for recommender systems. In recent times, different variants of deep learning algorithms have been explored in this setting to improve the task of…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…
Machine learning techniques for Recommendation System (RS) and Classification has become a prime focus of research to tackle the problem of information overload. RS are software tools that aim at making informed decisions about the services…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the…